I want to show different object modes on two different windows in 3DView (Object Mode and Weight Paint
The simplest thing to do is just disable overlays on one of your viewports. Look on the right side (top or bottom, probably top) of your viewport for a button with a &quot;show overlays&quot; tooltip. Click it.
There may be some information you wish to see with overlays.  In that case, click the drop-down arrow to the right of the overlays button and, while in weight paint mode, set weight paint opacity to 0.  And, optionally, set fade inactive geometry to 0.0, or disable it.  Selected vertices while in vertex mode will still be drawn; wireframes in face mode will be drawn.